To convert \(1170^\circ\) to radians, follow these steps:

### 1. **Conversion Formula:**
   The conversion from degrees to radians is done using the formula:
   \[
   \text{Radians} = \text{Degrees} \times \left(\frac{\pi}{180^\circ}\right)
   \]

### 2. **Apply the Formula:**
   \[
   1170^\circ \times \left(\frac{\pi}{180^\circ}\right) = \frac{1170\pi}{180}
   \]

### 3. **Simplify the Fraction:**
   Simplify \(\frac{1170\pi}{180}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 90:
   \[
   \frac{1170\pi}{180} = \frac{1170 \div 90 \pi}{180 \div 90} = \frac{13\pi}{2}
   \]

So, \(1170^\circ\) is equal to \(\frac{13\pi}{2}\) radians.

Would you like more details or have any questions about this conversion?

Here are some related questions for further practice:

1. How do you convert radians back to degrees?
2. What is the radian measure of a full circle (360°)?
3. How can you use the unit circle to visualize the angle \(\frac{13\pi}{2}\)?
4. What is the smallest positive coterminal angle of \(\frac{13\pi}{2}\) radians?
5. How do you express \(1170^\circ\) as a sum of a full circle and an additional angle?

**Tip:** When converting between degrees and radians, always remember that \(180^\circ\) equals \(\pi\) radians. This relationship is the key to quick and accurate conversions.

Learn how to convert 1170 degrees to radians using the conversion formula. Follow our detailed step-by-step guide with examples and practice questions. Ideal for high school students studying trigonometry and radians conversion.

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